Question: What is the sum of the the roots of the equation $4x^3 + 5x^2 - 8x = 0$? Express your answer as a decimal to the nearest hundredth.
Answer: First we can factor out an $x$. That gives us the equation $x(4x^2 + 5x - 8) = 0$. This product is equal to zero when $x = 0$ or when $(4x^2 + 5x - 8) = 0$. This root of zero contributes nothing to the sum of the roots. Now we don't actually need to factor $4x^2 + 5x - 8 = 0$ into the product of two binomials to find the sum of the roots. (It doesn't factor nicely.) If we divide both sides of this equation by 4, we get $x^2
+ (5/4)x - 2 = 0$. The coefficient of the middle term (5/4) is the opposite of the sum of the roots, so our answer is $\boxed{-1.25}$.